The North Greenland Icecore Project (NorthGRIP) palaeoclimatic information back to about 120 kyr BP. The size distributions of ice crystals in the upper 880 m of the NorthGRIP ice core, which cover a time-span of approximately 5300 years, have been obtained previously. The distributions evolve towards a universal curve, indicating a common underlying physical process in the formation of crystals. We identify this process as an interplay between fragmentation of the crystals and diffusion of their grain boundaries. The process is described by a two-parameter differential equation to which we obtain the exact solution. The solution is in excellent agreement with the measured distributions.